Transducers of this character are frequently used in precision-type instruments of physics laboratories, electromedical equipment, geological probes, military installations such as sonar devices, and sound-recording apparatus.
The capacitance of such a condenser, varying as a function of time in the presence of a sinusoidal acoustic wave, is given by EQU C(t)=C.sub.0 C.sub.1 sin .omega.t
where C.sub.0 is the magnitude of the static capacitance of the condenser and C.sub.1 is the increment resulting from an acoustic wave of given intensity and pulsatance .omega.t=2.pi.f. The maximum ratio C.sub.1 /C.sub.0 is generally very low, on the order of 10.sup.-4 /3.
Conventionally, the pressure-sensitive condenser is connected across a source of d-c voltage in series with a load resistor across which an output signal is available. The circuit resistance R, which includes the load resistor as well as the relatively minor internal resistance of the source, is traversed by a current i given by the equation ##EQU1## where E is the terminal voltage of the d-c source; see Physical Review 1917, Vol. X, No. 1, page 39. This equation can be solved for i to yield EQU I=.SIGMA.I.sub.n sin (n.omega.t+.phi..sub.n) (2)
where n is 1, 2, 3 etc. Considering only the first two terms, for which n=1 and n=2, one obtains ##EQU2## the higher-order terms, omitted in equation (3), are of progressively diminishing amplitudes.
Theoretically, therefore, the electrical output signal appearing across the load resistor has an infinite number of harmonics distorting its waveform. The ratio between the second harmonic (n=2) to the fundamental (n=1) is given, according to equation (3), by ##EQU3## which tends to C.sub.1 /2C.sub.0 for 2R&gt;1/.omega.C.sub.0. That ratio, accordingly, increases with the dynamic range .+-.C.sub.1 /C.sub.0 of the pressure-sensitive condenser. On the other hand, the aforementioned low value of this dynamic range necessitates the availability of a rather elevated d-c biasing voltage E (e.g. of 50 to 100 volts) in order to produce a useful output signal.